Assessing heterogeneous effects and their determinants via estimation of potential outcomes

When analyzing effect heterogeneity, the researcher commonly opts for stratification or a regression model with interactions. While these methods provide valuable insights, their usefulness can be somewhat limited, since they typically fail to take into account heterogeneity with respect to many dimensions simultaneously, or give rise to models with complex appearances. Based on the potential outcomes framework and through imputation of missing potential outcomes, our study proposes a method for analyzing heterogeneous effects by focusing on treatment effects rather than outcomes. The procedure is easy to implement and generates estimates that take into account heterogeneity with respect to all relevant dimensions at the same time. Results are easily interpreted and can additionally be represented by graphs, showing the overall magnitude and pattern of heterogeneity as well as how this relates to different factors. We illustrate the method both with simulations and by examining heterogeneous effects of obesity on HDL cholesterol in the Malmo Diet and Cancer cardiovascular cohort. Obesity was associated with reduced HDL in almost all individuals, but effects varied with smoking, risky alcohol consumption, higher education, and energy intake, with some indications of non-linear effects. Our approach can be applied by any epidemiologist who wants to assess the role and strength of heterogeneity with respect to a multitude of factors.